What you are trying to do is as the hand goes up to the next phrase, the pedal remains down but lifts and depresses quickly after the first note of the next phrase is started. This is bound to sound very clumsy because showing it would be more beneficial. The aim is basically to make a piece of music sound smooth without sounding muddy or cluttered. Over-use of the pedal can produce this result.
I have found that as I progressed as a musician, you tend to use your pedal almost instinctively. Make the sound smooth but not muddy.
That said, syncopated pedaling is a very important technique to learn and is particularly useful in more modern music, especially church music, and larger scale romantic works.
Tread carefully..... (get it??)
See what Gieseking has to say about treading in time.....